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Question

A sum of ₹69,300 is to be divided between two friends Michel and Vivian. They are 11 and 12 years old respectively. Their respective portions are compounded annually at 10% per annum. If they get the same amount when they are 24 years old, what is the share of Vivian?

A
₹ 36,300
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B
₹ 33,000
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C
₹ 34,000
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D
₹ 35,300
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Solution

The correct option is A ₹ 36,300
Let the share of Michel be ₹x.

Share of Vivian = ₹(69,300- x)

Time period for Vivian = final age – initial age = 24 – 12 = 12 years
Time period for Michel = final age – initial age = 24 – 11 = 13 years

Amount received by Michel after 13 years = P(1+R100)n = x(1+10100)13

And, the amount received by Vivian after 12 years = P(1+R100)n

= (69,300x)(1+10100)12

As per the question, both of them will get the same amount of money when they are 24 years old.

So, x(1+10100)13=(69,300x)(1+10100)12

x(110100) = 69,300x
110x=100(69,300x)
110x+100x=6,93,00,00
x=33,000
So, share of Michel = 33,000
Share of Vivian = (69,30033,000) = 36,300

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